A. Overview of An Exemplary Acousto-Optic Filter
Wavelength division multiplexing technology (e.g., Wavelength Division Multiplexing (WDM), Dense Wavelength Division Multiplexing (DWDM), etc.) involves the launching of a plurality of communication signals over a single optical fiber, wherein, each communication signal has its own associated optical wavelength. As such, the signal processing associated with wavelength division multiplexing technology involves the ability to process a particular communication signal at its own associated optical wavelength (or optical wavelength range).
An acousto-optic filter is a type of filter that can be “tuned” so as to filter the optical passband of an optical fiber at a specific optical wavelength. Thus, for example, an acousto-optic filter can be used to filter a single WDM/DWDM communication signal from a group of WDM/DWDM communication signals that exist on the same optical fiber. That is, the passage of optical energy being carried by the optical fiber at a specific optical wavelength (or a specific optical wavelength range) is attenuated. As a result, the strength of one or more communication signals that fall within the range of the filtered optical wavelength(s) is reduced. Reducing the strength of a communication signal can be useful if the signal is part of an overall equalization scheme.
An acousto-optic filter includes an excitation element that launches an acoustic wave along an optical fiber. The acoustic wave affects the optical properties of the optical fiber so that the optical signal strength(s) that reside at specific optical wavelength(s) is (are) attenuated. FIG. 1a shows an example of an acousto-optic filter. A continuous optical fiber is shown in FIG. 1a as having at least three sections 104a, 104b and 104c. A first section 104a of the optical fiber effectively acts as the input node to the filter; and, a third section 104c of the optical fiber effectively acts as the output node from the filter. A second section 104b of the optical fiber (which may also be referred to as the “acousto-optic interaction” section), as seen in FIG. 1a, is the section of the fiber that propagates an acoustic wave.
A transducing ring 101 that is made of piezo-electric material (e.g., PbZrT (PZT), PbMnN, etc.) and a horn 102 (which is often made of Aluminum (Al) or glass or other metals or ceramics) can be integrated together to form an excitation element that launches the acoustic wave onto the second optical fiber section 104b. A damper 103 absorbs acoustic wave energy so that the fiber section 104c that acts as the filter output may be kept physically rigid.
As a result of the activity of the excitation element, as seen in FIG. 1a, an acoustic wave is formed on the acousto-optic interaction fiber section 104b that propagates in the +z direction. The acoustic wave has a wavelength λf and an amplitude B. The wavelength λf and the amplitude B of the acoustic wave are a function of the properties of the transducing ring 101, the properties of the horn 102 and the amplitude and frequency of an electronic signal that is provided to the transducing ring 101 by an electronic signal source 105 (e.g., a voltage signal source) as briefly described immediately below.
In the exemplary embodiment of FIG. 1a, the electronic signal that is provided by the electronic signal source 105 has been expressed as Acos(2πfst). By positioning the leads that carry the electronic signal across the thickness “T” of the transducing ring 101, the electronic signal will induce a time-varying electric field across the transducing ring 101 (e.g., along the z axis as drawn in FIG. 1a). The transducing ring 101, being made of piezo-electric material, will “vibrate” in response. The direction of the vibrational response depends upon the “polling direction” of the transducing ring.
A polling direction is a property of piezo-electric material that indicates along which direction a piezo-electric stress can be induced. For example, if transducing ring 101 of FIG. 1a has its polling direction set along the y axis, the transducing ring 101 will vibrate along the y axis. That is, the dimension of the transducing ring 101 along the y axis will change with time. For example, in response to an oscillating electric field of frequency fs along the z axis, the transducing ring's height dimension “H”, as drawn in FIG. 1a, will oscillate (also at a frequency of fs) between some minimum height and some maximum height.
The amplitude of the transducing ring's stress is a function of the amplitude of the applied electric field; which, in turn, is a function of the amplitude “A” of the electronic signal Acos(2πfst). As such, according to the exemplary embodiment of FIG. 1a, the electronic signal determines both the frequency and the amplitude of the stress experienced by the transducing ring 101. The transducing ring 101 described just above can be referred to as a “shear mode” transducing ring because its polling direction is perpendicular to the direction of the applied electric field. Other transducing ring embodiments may have alternate polling directions (such as a thickness mode transducing ring having a thickness that varies with time).
The horn 102, as a result of its conical shape, amplifies the transducing ring's vibration and propagates it onto the acousto-optic interaction optical fiber section 104b. As an example of this amplification, the tip of the cone 120 can be made to vibrate with an amplitude of 100.0 nm and a frequency of fs if the cone 102 has an acoustic gain of 103 and the transducing ring 101 and electronic signal combine to produce a 0.1 nm transducing ring 101 stress that oscillates at a frequency of fs. 
This vibration is then transferred to the acousto-optic interaction fiber section 104b at the tip of the cone 120 (which causes the fiber to propagate an acoustic wave of approximately the same amplitude and frequency in the +z direction). The wavelength λf of the acoustic wave is a function of its velocity “v” and its frequency fs (i.e, λf=v/fs, where the velocity “v” is a function of the material composition of the optical fiber and its surrounding medium (such as a vacuum)). As discussed above, the amplitude of the acoustic wave B is a function of the amplitude A of the electronic signal. FIG. 1b shows an exemplary optical transfer function 106 for the acousto-optic filter that results from the acousto-optic wave observed in FIG. 1a. 
According to the transfer function 106 of FIG. 1b, the wavelength λf of the acoustic wave of FIG. 1a determines which optical frequency λO is filtered; and, the amplitude B of the acoustic wave of FIG. 1a determines the extent 107 to which the optical frequency λo is attenuated. Better said, according to the transfer function 106 of FIG. 1b, optical frequencies other than λo are more easily passed through the acousto-optic interaction portion of the optical fiber 104b with a relatively high transmission of T1.
However, optical frequencies at or near λo (as represented by point 107 in FIG. 1b) are passed along the acousto-optic interaction section 104b of the optical fiber with a relatively low transmission of T2 (which corresponds to high attenuation). By varying the frequency fs of the electronic signal provided to the transducing ring 101, the attenuation frequency λo can be made to vary; and, by varying the amplitude of the electronic signal A, the extent of the optical attenuation can be made to vary. Thus, by controlling the frequency fs and amplitude A of the electrical signal, the optical transfer function 106 of an acousto-optic filter can be “tuned” so as to prescribe a particular attenuation for a particular optical wavelength.
B. Reflections in Acousto-Optic Filters
A problem with acousto-optic filters is the presence of acoustic reflections that propagate along the acousto-optic interaction portion 104b of the optical fiber. As is known in the art, a change in the transportation medium of a wave induces a reflection of that wave. Thus, when an acoustic wave traveling in the +z direction along the acousto-optic interaction portion 104b of the fiber impinges upon the damper 103, a reflected wave is induced along the acousto-optic interaction portion 104b that travels in the −z direction. A portion of this reflected wave may then be reflected in the +z direction at the tip 120 of the cone 102.
Those of ordinary skill will recognize that the above described phenomena will cause “interaction” between the originally launched and reflected waves suitable for the establishment of a “standing wave” or “beating” on the second optical fiber portion 104b. Beating of the second harmonic type corresponds to amplitude fluctuation over time. An exemplary depiction of an acoustic-optic wave as it experiences beating of the second harmonic type is shown in FIG. 2a. Note that the acoustic wave is drawn as having: 1) a first amplitude at a first moment in time t1 (with solid line 204b1); and 2) a second amplitude at a second moment in time t2 (with dashed line 204b2). Consistent with the dynamics of acousto-optic filtering as discussed in the preceding section, a variation in acoustic wave amplitude, which also corresponds to time varying acousto-optic wave energy, will result in time varying attenuation through the filter for signals having wavelength λO.
The variation in attenuation, which may also be referred to as optical intensity modulation, is observed in the transfer function 206 of FIG. 2b by a pair of profiles: 1) a first (solid) profile 207 having greater attenuation (e.g., as associated with solid acoustic wave 204b1 of FIG. 2a); and 2) a second (dashed) profile 209 having lesser attenuation (e.g., as associated with dashed acoustic wave 204b2 of FIG. 2b). This fluctuation in attenuation corresponds to inconsistent filtering and thus can lead to inconsistent signal processing of wavelength division multiplexed signals.